Mathematical modeling predicts that endemics by generalist insects are eradicated if nearly all plants produce constitutive defense

Plants with constitutive defense chemicals exist widely in nature. The phenomenon is backed by abundant data from plant chemical ecology. Sufficient data are also available to conclude that plant defenses act as deterrent and repellent to attacking herbivores, particularly deleterious generalist insects. In the wild, generalist species are usually not endemic, meaning they are not restricted to certain plant species in a region. Therefore, our objective is to inspect theoretically whether evolution of chemical defenses in all plant species eradicate an endemic by any generalist species. The objective is addressed by developing deterministic ordinary differential equations under the following conditions: Plants without constitutive defenses are susceptible to oviposition by generalist insects, while they become defended against generalists by storing chemical defenses. From the models, we explicitly obtain that a generalist-free stable state is only possible if the vast majority of all plant individuals have chemical defenses. The model also allows one to predict the highest possible percentage of undefended plant individuals, which may be considered as free-riders.